.TH std::hypot,std::hypotf,std::hypotl 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::hypot,std::hypotf,std::hypotl \- std::hypot,std::hypotf,std::hypotl

.SH Synopsis
   Defined in header <cmath>
   float       hypot ( float x, float y );

   double      hypot ( double x, double y );          \fI(since C++11)\fP
                                                      (until C++23)
   long double hypot ( long double x, long
   double y );
   /* floating-point-type */

               hypot ( /* floating-point-type         (since C++23)
   */ x,                                              (constexpr since
                                                      C++26)
                       /* floating-point-type
   */ y );
                                                      \fI(since C++11)\fP
   float       hypotf( float x, float y );        \fB(2)\fP (constexpr since
                                                      C++26)
   long double hypotl( long double x, long            \fI(since C++11)\fP
   double y );                                    \fB(3)\fP (constexpr since
                                                      C++26)
   float       hypot ( float x, float y,
   float z );

   double      hypot ( double x, double y,                             \fI(since C++17)\fP
   double z );                                                         (until C++23)

   long double hypot ( long double x, long    \fB(1)\fP
   double y, long double z );
   /* floating-point-type */

               hypot ( /* floating-point-type
   */ x,                                                               (since C++23)
                       /* floating-point-type                          (constexpr since
   */ y,                                                               C++26)

                       /* floating-point-type     \fB(4)\fP
   */ z );
   Additional overloads
   Defined in header <cmath>
   template< class Arithmetic1, Arithmetic2 >
                                                                       \fI(since C++11)\fP
   /* common-floating-point-type */                   (A)              (constexpr since
                                                                       C++26)
               hypot ( Arithmetic1 x,
   Arithmetic2 y );
   template< class Arithmetic1, Arithmetic2,
   Arithmetic3 >
                                                                       \fI(since C++17)\fP
   /* common-floating-point-type */                   (B)              (constexpr since
                                                                       C++26)
               hypot ( Arithmetic1 x,
   Arithmetic2 y, Arithmetic3 z );

   1-3) Computes the square root of the sum of the squares of x and y, without undue
   overflow or underflow at intermediate stages of the computation.
   The library provides overloads of std::hypot for all cv-unqualified floating-point
   types as the type of the parameters x and y.
   (since C++23)
   4) Computes the square root of the sum of the squares of x, y, and z, without undue
   overflow or underflow at intermediate stages of the computation.
   The library provides overloads of std::hypot for all cv-unqualified floating-point
   types as the type of the parameters x, y and z.
   (since C++23)
   A,B) Additional overloads are provided for all other combinations of arithmetic
   types.

   The value computed by the two-argument version of this function is the length of the
   hypotenuse of a right-angled triangle with sides of length x and y, or the distance
   of the point (x,y) from the origin (0,0), or the magnitude of a complex number x+iy.

   The value computed by the three-argument version of this function is the distance of
   the point (x,y,z) from the origin (0,0,0).

.SH Parameters

   x, y, z - floating-point or integer values

.SH Return value

   1-3,A) If no errors occur, the hypotenuse of a right-angled triangle,
   \\(\\scriptsize{\\sqrt{x^2+y^2} }\\)
   √
   x2
   +y2
   , is returned.
   4,B) If no errors occur, the distance from origin in 3D space,
   \\(\\scriptsize{\\sqrt{x^2+y^2+z^2} }\\)
   √
   x2
   +y2
   +z2
   , is returned.

   If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is
   returned.

   If a range error due to underflow occurs, the correct result (after rounding) is
   returned.

.SH Error handling

   Errors are reported as specified in math_errhandling.

   If the implementation supports IEEE floating-point arithmetic (IEC 60559),

     * std::hypot(x, y), std::hypot(y, x), and std::hypot(x, -y) are equivalent.
     * if one of the arguments is ±0, std::hypot(x, y) is equivalent to std::fabs
       called with the non-zero argument.
     * if one of the arguments is ±∞, std::hypot(x, y) returns +∞ even if the other
       argument is NaN.
     * otherwise, if any of the arguments is NaN, NaN is returned.

.SH Notes

   Implementations usually guarantee precision of less than 1 ulp (Unit in the Last
   Place — Unit of Least Precision): GNU, BSD.

   std::hypot(x, y) is equivalent to std::abs(std::complex<double>(x, y)).

   POSIX specifies that underflow may only occur when both arguments are subnormal and
   the correct result is also subnormal (this forbids naive implementations).

   Distance between two points (x1,y1,z1) and (x2,y2,z2) on 3D space can
   be calculated using 3-argument overload of std::hypot as std::hypot(x2 \fI(since C++17)\fP
   - x1, y2 - y1, z2 - z1).

   The additional overloads are not required to be provided exactly as (A,B). They only
   need to be sufficient to ensure that for their first argument num1, second argument
   num2 and the optional third argument num3:

     * If num1, num2 or num3 has type long double, then

     * std::hypot(num1, num2) has the same effect as
       std::hypot(static_cast<long double>(num1),
                  static_cast<long double>(num2)), and
     * std::hypot(num1, num2, num3) has the same effect as
       std::hypot(static_cast<long double>(num1),
                  static_cast<long double>(num2),
                  static_cast<long double>(num3)).
     * Otherwise, if num1, num2 and/or num3 has type double or an integer
       type, then

     * std::hypot(num1, num2) has the same effect as
       std::hypot(static_cast<double>(num1),                              (until C++23)
                  static_cast<double>(num2)), and
     * std::hypot(num1, num2, num3) has the same effect as
       std::hypot(static_cast<double>(num1),
                  static_cast<double>(num2),
                  static_cast<double>(num3)).
     * Otherwise, if num1, num2 or num3 has type float, then

     * std::hypot(num1, num2) has the same effect as
       std::hypot(static_cast<float>(num1),
                  static_cast<float>(num2)), and
     * std::hypot(num1, num2, num3) has the same effect as
       std::hypot(static_cast<float>(num1),
                  static_cast<float>(num2),
                  static_cast<float>(num3)).
   If num1, num2 and num3 have arithmetic types, then

     * std::hypot(num1, num2) has the same effect as
       std::hypot(static_cast</* common-floating-point-type */>(num1),
                  static_cast</* common-floating-point-type */>(num2)),
       and
     * std::hypot(num1, num2, num3) has the same effect as
       std::hypot(static_cast</* common-floating-point-type */>(num1),
                  static_cast</* common-floating-point-type */>(num2),
                  static_cast</* common-floating-point-type */>(num3)),   (since C++23)

   where /* common-floating-point-type */ is the floating-point type with
   the greatest floating-point conversion rank and greatest
   floating-point conversion subrank among the types of num1, num2 and
   num3, arguments of integer type are considered to have the same
   floating-point conversion rank as double.

   If no such floating-point type with the greatest rank and subrank
   exists, then overload resolution does not result in a usable candidate
   from the overloads provided.

   Feature-test macro  Value    Std                Feature
   __cpp_lib_hypot    201603L \fI(C++17)\fP 3-argument overload of std::hypot

.SH Example


// Run this code

 #include <cerrno>
 #include <cfenv>
 #include <cfloat>
 #include <cmath>
 #include <cstring>
 #include <iostream>

 // #pragma STDC FENV_ACCESS ON

 struct Point3D { float x, y, z; };

 int main()
 {
     // typical usage
     std::cout << "(1,1) cartesian is (" << std::hypot(1,1)
               << ',' << std::atan2(1,1) << ") polar\\n";

     Point3D a{3.14, 2.71, 9.87}, b{1.14, 5.71, 3.87};
     // C++17 has 3-argument hypot overload:
     std::cout << "distance(a,b) = "
               << std::hypot(a.x - b.x, a.y - b.y, a.z - b.z) << '\\n';

     // special values
     std::cout << "hypot(NAN,INFINITY) = " << std::hypot(NAN, INFINITY) << '\\n';

     // error handling
     errno = 0;
     std::feclearexcept(FE_ALL_EXCEPT);
     std::cout << "hypot(DBL_MAX,DBL_MAX) = " << std::hypot(DBL_MAX, DBL_MAX) << '\\n';

     if (errno == ERANGE)
         std::cout << "    errno = ERANGE " << std::strerror(errno) << '\\n';
     if (std::fetestexcept(FE_OVERFLOW))
         std::cout << "    FE_OVERFLOW raised\\n";
 }

.SH Output:

 (1,1) cartesian is (1.41421,0.785398) polar
 distance(a,b) = 7
 hypot(NAN,INFINITY) = inf
 hypot(DBL_MAX,DBL_MAX) = inf
     errno = ERANGE Numerical result out of range
     FE_OVERFLOW raised

.SH See also

   pow
   powf              raises a number to the given power (\\(\\small{x^y}\\)x^y)
   powl              \fI(function)\fP
   \fI(C++11)\fP
   \fI(C++11)\fP
   sqrt              computes square root (\\(\\small{\\sqrt{x}}\\)
   sqrtf             √
   sqrtl             x)
   \fI(C++11)\fP           \fI(function)\fP
   \fI(C++11)\fP
   cbrt              computes cube root (\\(\\small{\\sqrt[3]{x}}\\)
   cbrtf             3
   cbrtl             √
   \fI(C++11)\fP           x)
   \fI(C++11)\fP           \fI(function)\fP
   \fI(C++11)\fP
   abs(std::complex) returns the magnitude of a complex number
                     \fI(function template)\fP
   C documentation for
   hypot
